Generative Adversarial Networks (GANs) have received wide acclaim among the machine learning (ML) community for their ability to generate realistic 2D images. ML is being applied more often to complex problems beyond those of computer vision. However, current frameworks often serve as black boxes and lack physics embeddings, leading to poor ability in enforcing constraints and unreliable models. In this work, we develop physics embeddings that can be stringently imposed, referred to as hard constraints, in the neural network architecture. We demonstrate their capability for 3D turbulence by embedding them in GANs, particularly to enforce the mass conservation constraint in incompressible fluid turbulence. In doing so, we also explore and contrast the effects of other methods of imposing physics constraints within the GANs framework, especially penalty-based physics constraints popular in literature. By using physics-informed diagnostics and statistics, we evaluate the strengths and weaknesses of our approach and demonstrate its feasibility.

在整个计算科学中，越来越需要利用原始计算马力的持续改进，通过对蛮力的尺度锻炼的尺度增加，以增加网状元素数量的增加。例如，如果不考虑分子水平的相互作用，就不可能对纳米多孔介质的转运进行定量预测，即从紧密的页岩地层提取至关重要的碳氢化合物。同样，惯性限制融合模拟依赖于数值扩散来模拟分子效应，例如非本地转运和混合，而无需真正考虑分子相互作用。考虑到这两个不同的应用程序，我们开发了一种新颖的功能，该功能使用主动学习方法来优化局部细尺度模拟的使用来告知粗尺度流体动力学。我们的方法解决了三个挑战：预测连续性粗尺度轨迹，以推测执行新的精细分子动力学计算，动态地更新细度计算中的粗尺度，并量化神经网络模型中的不确定性。

语言模型既展示了定量的改进，又展示了新的定性功能，随着规模的增加。尽管它们具有潜在的变革性影响，但这些新能力的特征却很差。为了为未来的研究提供信息，为破坏性的新模型能力做准备，并改善社会有害的效果，至关重要的是，我们必须了解目前和近乎未来的能力和语言模型的局限性。为了应对这一挑战，我们介绍了超越模仿游戏基准（Big Bench）。 Big Bench目前由204个任务组成，由132家机构的442位作者贡献。任务主题是多样的，从语言学，儿童发展，数学，常识性推理，生物学，物理学，社会偏见，软件开发等等。 Big-Bench专注于被认为超出当前语言模型的功能的任务。我们评估了OpenAI的GPT型号，Google内部密集变压器体系结构和大型基础上的开关稀疏变压器的行为，跨越了数百万到数十亿个参数。此外，一个人类专家评估者团队执行了所有任务，以提供强大的基准。研究结果包括：模型性能和校准都随规模改善，但绝对的术语（以及与评估者的性能相比）；在模型类中的性能非常相似，尽管带有稀疏性。逐渐和预测的任务通常涉及大量知识或记忆成分，而在临界规模上表现出“突破性”行为的任务通常涉及多个步骤或组成部分或脆性指标；社交偏见通常会随着含糊不清的环境而随着规模而增加，但这可以通过提示来改善。

我们建议采用统计回归作为投影操作员，以使数据驱动以数据为基础的Mori-Zwanzig形式主义中的运营商学习。我们提出了一种原则性方法，用于为任何回归模型提取Markov和内存操作员。我们表明，线性回归的选择导致了基于Mori的投影操作员最近提出的数据驱动的学习算法，这是一种高阶近似Koopman学习方法。我们表明，更具表现力的非线性回归模型自然填补了高度理想化和计算有效的MORI投影操作符和最佳迄今为止计算上最佳的Zwanzig投影仪之间的差距。我们进行了数值实验，并提取了一系列基于回归的投影的运算符，包括线性，多项式，样条和基于神经网络的回归，随着回归模型的复杂性的增加而显示出渐进的改进。我们的命题提供了一个通用框架来提取内存依赖性校正，并且可以轻松地应用于文献中固定动力学系统的一系列数据驱动的学习方法。

湍流无处不在，获得有效，准确且可概括的订单模型仍然是一个具有挑战性的问题。该手稿开发了减少拉格朗日模型的湍流模型的层次结构，以研究和比较在拉格朗日框架内实施平滑的粒子流体动力学（SPH）结构与嵌入神经网络（NN）作为通用函数近似器中的效果。 SPH是用于近似流体力学方程的无网格拉格朗日方法。从基于神经网络（NN）的拉格朗日加速运算符的参数化开始，该层次结构逐渐结合了一个弱化和参数化的SPH框架，该框架可以执行物理对称性和保护定律。开发了两个新的参数化平滑核，其中包含在完全参数化的SPH模拟器中，并与立方和四分之一的平滑核进行了比较。对于每个模型，我们使用基于梯度的优化最小化的不同损耗函数，其中使用自动分化（AD）和灵敏度分析（SA）获得了有效的梯度计算。每个模型均经过两个地面真理（GT）数据集训练，该数据集与每周可压缩的均质各向同性湍流（hit），（1）使用弱压缩SPH的验证集，（2）来自直接数值模拟（DNS）的高忠诚度集。数值证据表明：（a）对“合成” SPH数据的方法验证； （b）嵌入在SPH框架中近似状态方程的NN的能力； （b）每个模型都能插入DNS数据； （c）编码更多的SPH结构可提高对不同湍流的马赫数和时间尺度的普遍性； （d）引入两个新型参数化平滑核可提高SPH比标准平滑核的准确性。

The performance of inertial navigation systems is largely dependent on the stable flow of external measurements and information to guarantee continuous filter updates and bind the inertial solution drift. Platforms in different operational environments may be prevented at some point from receiving external measurements, thus exposing their navigation solution to drift. Over the years, a wide variety of works have been proposed to overcome this shortcoming, by exploiting knowledge of the system current conditions and turning it into an applicable source of information to update the navigation filter. This paper aims to provide an extensive survey of information aided navigation, broadly classified into direct, indirect, and model aiding. Each approach is described by the notable works that implemented its concept, use cases, relevant state updates, and their corresponding measurement models. By matching the appropriate constraint to a given scenario, one will be able to improve the navigation solution accuracy, compensate for the lost information, and uncover certain internal states, that would otherwise remain unobservable.

We consider infinite horizon Markov decision processes (MDPs) with fast-slow structure, meaning that certain parts of the state space move "fast" (and in a sense, are more influential) while other parts transition more "slowly." Such structure is common in real-world problems where sequential decisions need to be made at high frequencies, yet information that varies at a slower timescale also influences the optimal policy. Examples include: (1) service allocation for a multi-class queue with (slowly varying) stochastic costs, (2) a restless multi-armed bandit with an environmental state, and (3) energy demand response, where both day-ahead and real-time prices play a role in the firm's revenue. Models that fully capture these problems often result in MDPs with large state spaces and large effective time horizons (due to frequent decisions), rendering them computationally intractable. We propose an approximate dynamic programming algorithmic framework based on the idea of "freezing" the slow states, solving a set of simpler finite-horizon MDPs (the lower-level MDPs), and applying value iteration (VI) to an auxiliary MDP that transitions on a slower timescale (the upper-level MDP). We also extend the technique to a function approximation setting, where a feature-based linear architecture is used. On the theoretical side, we analyze the regret incurred by each variant of our frozen-state approach. Finally, we give empirical evidence that the frozen-state approach generates effective policies using just a fraction of the computational cost, while illustrating that simply omitting slow states from the decision modeling is often not a viable heuristic.

In the present work we propose an unsupervised ensemble method consisting of oblique trees that can address the task of auto-encoding, namely Oblique Forest AutoEncoders (briefly OF-AE). Our method is a natural extension of the eForest encoder introduced in [1]. More precisely, by employing oblique splits consisting in multivariate linear combination of features instead of the axis-parallel ones, we will devise an auto-encoder method through the computation of a sparse solution of a set of linear inequalities consisting of feature values constraints. The code for reproducing our results is available at https://github.com/CDAlecsa/Oblique-Forest-AutoEncoders.

When robots learn reward functions using high capacity models that take raw state directly as input, they need to both learn a representation for what matters in the task -- the task ``features" -- as well as how to combine these features into a single objective. If they try to do both at once from input designed to teach the full reward function, it is easy to end up with a representation that contains spurious correlations in the data, which fails to generalize to new settings. Instead, our ultimate goal is to enable robots to identify and isolate the causal features that people actually care about and use when they represent states and behavior. Our idea is that we can tune into this representation by asking users what behaviors they consider similar: behaviors will be similar if the features that matter are similar, even if low-level behavior is different; conversely, behaviors will be different if even one of the features that matter differs. This, in turn, is what enables the robot to disambiguate between what needs to go into the representation versus what is spurious, as well as what aspects of behavior can be compressed together versus not. The notion of learning representations based on similarity has a nice parallel in contrastive learning, a self-supervised representation learning technique that maps visually similar data points to similar embeddings, where similarity is defined by a designer through data augmentation heuristics. By contrast, in order to learn the representations that people use, so we can learn their preferences and objectives, we use their definition of similarity. In simulation as well as in a user study, we show that learning through such similarity queries leads to representations that, while far from perfect, are indeed more generalizable than self-supervised and task-input alternatives.

While the capabilities of autonomous systems have been steadily improving in recent years, these systems still struggle to rapidly explore previously unknown environments without the aid of GPS-assisted navigation. The DARPA Subterranean (SubT) Challenge aimed to fast track the development of autonomous exploration systems by evaluating their performance in real-world underground search-and-rescue scenarios. Subterranean environments present a plethora of challenges for robotic systems, such as limited communications, complex topology, visually-degraded sensing, and harsh terrain. The presented solution enables long-term autonomy with minimal human supervision by combining a powerful and independent single-agent autonomy stack, with higher level mission management operating over a flexible mesh network. The autonomy suite deployed on quadruped and wheeled robots was fully independent, freeing the human supervision to loosely supervise the mission and make high-impact strategic decisions. We also discuss lessons learned from fielding our system at the SubT Final Event, relating to vehicle versatility, system adaptability, and re-configurable communications.